\newproblem{lay:6_1_15}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 6.1.15}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $\mathbf{a}=\begin{pmatrix}8\\-5\end{pmatrix}$ and $\mathbf{b}=\begin{pmatrix}-2\\-3\end{pmatrix}$. Determine if both vectors are orthgonal.
}{
   % Solution
	$\mathbf{a}$ is orthogonal to $\mathbf{b}$ if their inner product is 0
	\begin{center}
		$\mathbf{a}\cdot \mathbf{b}=0$\\
		$8\cdot(-2)+(-5)\cdot(-3)=-16-15=-31\neq 0$
	\end{center}
	So, they are not orthogonal.
}
\useproblem{lay:6_1_15}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
